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Minimization of a particular singular value
2016 54th Annual Allerton Conference on Communication, Control, and Computing (Allerton), 2016We consider the problem of minimizing a particular singular value of a matrix variable, which is then subject to some convex constraints. Convex heuristics for this problem are discussed, including some counter-intuitive results regarding which is best, which then provide upper bounds on the value of the problem.
Alborz Alavian, Michael Rotkowitz
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Computation of the singular value expansion
Computing, 1988A method for computing the singular values and singular functions of real square-integrable kernels is presented. The analysis shows that a ``good'' discretization always yields a matrix whose singular value decomposition is closely related to the singular value expansion of the kernel.
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Singular Points and Singular Values of Mappings of Hilbert Manifolds
Journal of Mathematical Sciences, 2004zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jacquet, S., Sarychev, A.
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Bounds for the Singular Values of a Matrix
IMA Journal of Numerical Analysis, 1982A theorem of Gerschgorin type for finding bounds on singular values of a matrix is derived. In some cases it gives a good lower bound on the smallest singular value of a column scaled matrix. It is shown that this problem is interesting in finite difference applications, and a few numerical examples are given.
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A systematic derived sinh based method for singular and nearly singular boundary integrals
Engineering Analysis With Boundary Elements, 2021Wenliao Du, Xiaoyu Wen, Haoqi Wang
exaly